Filtration

Summary

A filtration is an increasing family $(\mathcal{F}_t)_{t \in T}$ of sub-$\sigma$-algebras of the $\sigma$-algebra of a probability space, indexed by time. The $\sigma$-algebra $\mathcal{F}_t$ models the information available at time $t$, and information is never lost as time goes on. Filtrations are the setting for adapted processes, stopping times and martingales.